The 6' has dimensions anyone over 25 or maybe 30 years old grew up surfing on & plenty of your crew continue to ride. Just gotta learn to read waves & take off less early than you would on longer board.Trade off is you will find your current 6' lot easier to duckdive & get out the back. Persevere & it will be rewarding after time dependent on how much you persevere
Or get a board that isn't as drastic a downsize. 6'4"x 20 1/2 x 2 1/2. Plenty like that around. A good surfer can throw any board around. Doesnt sound like the new board is doing you any favours.
But basically you are going to have to sit further in and take off later. And always paddle as hard as you can.
Is it an issue of the balance on the smaller board when taking off, not getting in early enough, missing the waves altogether or does it just feel like you don't get the same momentum padding around in general?
Switching to smaller boards can be frustrating at first, I have swapped between low 6' boards to mid lengths, Mal's and even a SUP, and all have their place and it is fun trying different boards - it takes the brain and the body a little to adjust to a different board, like muscle memory.
New SB's can be deceiving with how well they paddle when compared to the older SB's for the same size , is your smaller board a modern design? Don't buy 100% into the volume calculator as well - its a clever marketing tool IMO.